Proof: (R ⊂ κ(G, s)). Let I ⊂ M(G, s) be a nonempty ideal. Fix ψ ∈ I. Given σ ∈ R, there exists a sandpile φ such that σ = (φ + ψ)◦ by defintion. Since I is an ideal, this implies that σ ∈ I. Hence R ⊂ I. We conclude that R ⊂ ⋂ I ideal of M(G,s) I = κ(G, s). (κ(G, s) ⊂ R). Recall that R 6= ∅. Since κ(G, s) is the minimal ideal of M(G, s), it is enough to show that R is an ideal. Consider σ ∈ R ...

Let R be a ring and let I 6= R be an ideal of R. Then I is said to be a completely prime ideal of R if R/I is a domain and is said to be completely semiprime if R/I is a reduced ring. In this paper, we introduce a new class of rings known as completely prime ideal rings. We say that a ring R is a completely prime ideal ring (CPI-ring) if every prime ideal of R is completely prime. We say that a...

results in total, 80 food samples suspected of seb contamination were assessed using the two methods. fifty-four samples were contaminated based on the pcr technique and twenty-six of those were confirmed using the strip assay. conclusions the sensitivity of the sandwich method was approximately 10 ng/ml and that of the competitive method was approximately 250 ng/ml. in the lfd, a highly specif...

the subject of transplant immunosuppression has generated significant interest in recent years. excellent immunosuppression, advances in surgical technique, post-transplantation care, and infection control have resulted in excellent outcomes. there is widespread support for the notion that the fundamental objective in transplant immunology should be the achievement of specific graft tolerance. ...

We introduce a specialization technique in order to study monomial ideals that are generated in degree two by using our earlier results about Ferrers ideals. It allows us to describe explicitly a cellular minimal free resolution of various ideals including any strongly stable and any squarefree strongly stable ideal whose minimal generators have degree two. In particular, this shows that thresh...

Given a zero-dimensional ideal I in a polynomial ring, many computations start by finding univariate polynomials in I . Searching for a univariate polynomial in I is a particular case of considering the minimal polynomial of an element in P/I . It is well known that minimal polynomials may be computed via elimination, therefore this is considered to be a “resolved problem”. But being the key of...

We prove that the 82 link complement is the minimal volume orientable hyperbolic manifold with 4 cusps. Its volume is twice of the volume V8 of the ideal regular octahedron, i.e. 7.32... = 2V8. The proof relies on Agol’s argument used to determine the minimal volume hyperbolic 3-manifolds with 2 cusps. We also need to estimate the volume of a hyperbolic 3-manifold with totally geodesic boundary...

In this paper we complete the algorithm DISPGB (Discussing Parametric Gröbner Basis) from the last paper by Montes, in order to obtain the Minimal Canonical Comprehensive Gröbner System (MCCGS). Given a parametric ideal, the MCCGS algorithm provides the minimal partition of the parameter space with associated Gröbner bases having the same type of solutions over each segment and provides a canon...

We describe a minimal set of generators of the defining ideal of the Rees Algebra associated to a proper parametrization of any monoid hypersurface. In the case of plane curves, we recover a known description for rational parametrizations having a syzygy of minimal degree (μ = 1). We also show that our approach can be applied to parametrizations of rational surfaces having a Hilbert-Burch resol...

The subject of transplant immunosuppression has generated significant interest in recent years. Excellent immunosuppression, advances in surgical technique, post-transplantation care, and infection control have resulted in excellent outcomes. There is widespread support for the notion that the fundamental objective in transplant immunology should be the achievement of specific graft toleran...